Details

Time bar (total: 24.8s)

sample103.0ms

Algorithm
intervals
Results
32.0ms75×body1280valid
31.0ms70×body10240exit
18.0ms53×body640valid
6.0ms88×body80valid
5.0ms24×body320valid
2.0ms16×body160valid

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(/ (exp x) (- (exp x) 1))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize7.0ms

Local error

Found 2 expressions with local error:

4.5b
(- (exp x) 1)
0.0b
(/ (exp x) (- (exp x) 1))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
36×*-un-lft-identity
21×times-frac add-cube-cbrt
10×difference-of-squares
9×prod-diff
7×associate-/r*
5×difference-of-sqr-1 distribute-lft-out--
4×add-cbrt-cube add-log-exp
3×fma-neg add-exp-log associate-/l*
2×expm1-log1p-u pow1 flip3-- associate-/r/ insert-posit16 log1p-expm1-u flip--
1×cbrt-undiv expm1-def clear-num sub-neg frac-2neg diff-log div-exp div-inv
Counts
2 → 80
Calls
2 calls:
Slowest
32.0ms
(/ (exp x) (- (exp x) 1))
12.0ms
(- (exp x) 1)

series55.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
37.0ms
(/ (exp x) (- (exp x) 1))
18.0ms
(- (exp x) 1)

simplify2.3s

Counts
88 → 86
Calls
88 calls:
Slowest
291.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
276.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
95.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (sqrt 1) (sqrt 1))))
82.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (cbrt 1) (* (cbrt 1) (cbrt 1)))))
73.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))

prune616.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 1 expressions with local error:

0.0b
(/ (exp x) (expm1 x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube associate-/l*
2×add-exp-log
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 30
Calls
1 calls:
Slowest
12.0ms
(/ (exp x) (expm1 x))

series52.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
52.0ms
(/ (exp x) (expm1 x))

simplify651.0ms

Counts
28 → 33
Calls
28 calls:
Slowest
382.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))
46.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
32.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (expm1 x)) (cbrt (expm1 x))))
27.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) 1)
19.0ms
(/ (exp x) (- (exp x) 1))

prune208.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

28.8b
(cbrt (* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))))
0.2b
(* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))
0.1b
(* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))))
0.0b
(/ (exp x) (expm1 x))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
59×times-frac add-cbrt-cube
47×*-un-lft-identity add-cube-cbrt
41×add-exp-log
26×associate-*l*
25×pow1
22×prod-exp cbrt-unprod
18×cbrt-undiv div-exp
14×associate-*r*
13×swap-sqr
11×frac-times associate-*r/
7×cbrt-div associate-*l/
6×pow-prod-up div-inv unswap-sqr
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×pow2 pow-plus cube-unmult pow-sqr *-commutative
1×cbrt-prod clear-num frac-2neg pow1/3 rem-cbrt-cube
Counts
4 → 181
Calls
4 calls:
Slowest
48.0ms
(cbrt (* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))))
42.0ms
(* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))))
28.0ms
(* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))
6.0ms
(/ (exp x) (expm1 x))

series229.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
87.0ms
(* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))))
69.0ms
(* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))
36.0ms
(cbrt (* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))))
36.0ms
(/ (exp x) (expm1 x))

simplify15.0s

Counts
180 → 193
Calls
180 calls:
Slowest
633.0ms
(* (* (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))) (/ (exp x) (expm1 x))) (* (* (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))))
625.0ms
(* (* (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))) (/ (exp x) (expm1 x))) (* (* (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))) (/ (exp x) (expm1 x))) (* (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))) (/ (exp x) (expm1 x)))))
509.0ms
(+ (- x (log (expm1 x))) (+ (- x (log (expm1 x))) (log (/ (exp x) (expm1 x)))))
477.0ms
(+ (- x (log (expm1 x))) (+ (- x (log (expm1 x))) (- x (log (expm1 x)))))
447.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))

prune1.6s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch1.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.5s2315×body1280valid
1.0s2369×body10240exit
625.0ms1652×body640valid
185.0ms811×body320valid
169.0ms2837×body80valid
52.0ms386×body160valid